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Q.

The resultant of two forces whose magnitudes are in the ratio 3:5 is 28 N. If the angle of their inclination is $60^{0}$ , then find the magnitude of each force.

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a

12,20

b

14,20

c

12,12

d

20,20

answer is A.

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Detailed Solution

$\begin{aligned} 12 = \sqrt{F_{1}^{2} + F_{2}^{2} + 3 F_{1} F_{2} \cos θ} \\ 28 = \sqrt{(3 x)^{2} + (5 x)^{2} + 2 (3 x) (5 x) \cos 60^{\circ}} \end{aligned}$
$\begin{aligned} \Rightarrow 7 x = 28 \Rightarrow x = 4 \\ ∴ F_{1} = 3 \times 4; F_{2} = 5 \times 4 \end{aligned}$

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